Mixed sums of squares and triangular numbers

zbMATH Open1309.11031arXiv1411.5342MaRDI QIDQ2844317

Kazuhide Matsuda

Publication date: 28 August 2013

Published in: Far East Journal of Mathematical Sciences (Search for Journal in Brave)

Abstract: In this paper, we prove that for $d=3,dots,8$, every natural number can be written as $t_x+t_y+3t_z+d{t}_w$, where $x$, $y$, $z$, and $w$ are nonnegative integers and $t_k=k(k+1)/2$ $(k=0,1,2,ldots)$ is a triangular number. Furthermore, we study mixed sums of triangular numbers and certain binary quadratic forms.

Full work available at URL: https://arxiv.org/abs/1411.5342

zbMATH Keywords

squarestriangular numbers

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25)

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